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NISM Certifications · NISM-Series-XV: Research Analyst · Fundamentals of Research

Which of the following is a limitation of using a simple average of past growth rates rather than a geometric mean to describe multi-year investment returns?

The arithmetic mean can overstate the compounded return when returns fluctuate widely. For instance, gains of 50% and then losses of 50% average zero, yet the investor ends with only 75% of the initial wealth. The geometric mean correctly reflects compounding and is preferred for multi-period returns.

  1. AThe arithmetic mean can overstate the compounded return when returns are volatileCorrect
  2. BThe arithmetic mean always understates compounded return
  3. CThe geometric mean ignores the effect of compounding
  4. DThe arithmetic mean cannot be computed for negative returns

Explanation

With volatile returns, the arithmetic average is higher than the geometric mean, so it overstates actual compounded growth. For example, +50% then -50% averages 0% but leaves wealth at 75% of the start. The geometric mean captures compounding.

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